↑

Properties

Label 158.6.c.a
Level $158$
Weight $6$
Character orbit 158.c
Analytic conductor $25.341$
Analytic rank $0$
Dimension $34$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [158,6,Mod(23,158)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("158.23"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(158, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 6, names="a")
 
Level: \( N \) \(=\) \( 158 = 2 \cdot 79 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 158.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [34,-68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(25.3406435305\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 68 q^{2} - 9 q^{3} - 272 q^{4} - 31 q^{5} - 36 q^{6} - 8 q^{7} + 2176 q^{8} - 1002 q^{9} + 248 q^{10} + 291 q^{11} + 288 q^{12} + 1447 q^{13} + 64 q^{14} + 798 q^{15} - 4352 q^{16} + 762 q^{17} + 8016 q^{18}+ \cdots - 133474 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
23.1 −2.00000 − 3.46410i −13.6586 − 23.6574i −8.00000 + 13.8564i 17.9261 − 31.0490i −54.6345 + 94.6297i 88.5343 − 153.346i 64.0000 −251.616 + 435.811i −143.409
23.2 −2.00000 − 3.46410i −12.8762 − 22.3023i −8.00000 + 13.8564i −34.0549 + 58.9848i −51.5049 + 89.2091i −41.6938 + 72.2158i 64.0000 −210.095 + 363.895i 272.439
23.3 −2.00000 − 3.46410i −11.1218 − 19.2635i −8.00000 + 13.8564i 6.81513 − 11.8042i −44.4872 + 77.0540i 73.6066 − 127.490i 64.0000 −125.888 + 218.045i −54.5211
23.4 −2.00000 − 3.46410i −9.90696 − 17.1594i −8.00000 + 13.8564i 8.00887 − 13.8718i −39.6278 + 68.6374i −109.901 + 190.355i 64.0000 −74.7957 + 129.550i −64.0710
23.5 −2.00000 − 3.46410i −6.72598 − 11.6497i −8.00000 + 13.8564i 39.4835 − 68.3875i −26.9039 + 46.5989i −39.5287 + 68.4657i 64.0000 31.0224 − 53.7324i −315.868
23.6 −2.00000 − 3.46410i −6.14246 − 10.6391i −8.00000 + 13.8564i −55.3341 + 95.8416i −24.5698 + 42.5562i 100.386 − 173.873i 64.0000 46.0404 − 79.7443i 442.673
23.7 −2.00000 − 3.46410i −4.12778 − 7.14953i −8.00000 + 13.8564i 30.3088 − 52.4963i −16.5111 + 28.5981i 10.2786 − 17.8031i 64.0000 87.4228 − 151.421i −242.470
23.8 −2.00000 − 3.46410i −1.10472 − 1.91344i −8.00000 + 13.8564i −18.4563 + 31.9672i −4.41889 + 7.65375i −36.3981 + 63.0433i 64.0000 119.059 − 206.217i 147.650
23.9 −2.00000 − 3.46410i 0.134824 + 0.233522i −8.00000 + 13.8564i −19.9279 + 34.5162i 0.539295 − 0.934087i 17.5054 − 30.3203i 64.0000 121.464 − 210.381i 159.423
23.10 −2.00000 − 3.46410i 1.19710 + 2.07343i −8.00000 + 13.8564i −3.30511 + 5.72462i 4.78839 − 8.29374i 54.0945 − 93.6944i 64.0000 118.634 − 205.480i 26.4409
23.11 −2.00000 − 3.46410i 2.10557 + 3.64696i −8.00000 + 13.8564i −39.2217 + 67.9339i 8.42230 − 14.5878i −122.799 + 212.695i 64.0000 112.633 − 195.086i 313.773
23.12 −2.00000 − 3.46410i 6.67137 + 11.5552i −8.00000 + 13.8564i 49.7680 − 86.2007i 26.6855 − 46.2206i 95.1824 − 164.861i 64.0000 32.4856 − 56.2667i −398.144
23.13 −2.00000 − 3.46410i 7.28016 + 12.6096i −8.00000 + 13.8564i 38.7713 − 67.1539i 29.1206 − 50.4384i −107.158 + 185.602i 64.0000 15.4985 − 26.8442i −310.170
23.14 −2.00000 − 3.46410i 7.54375 + 13.0662i −8.00000 + 13.8564i 8.07504 − 13.9864i 30.1750 − 52.2646i −36.9935 + 64.0746i 64.0000 7.68362 − 13.3084i −64.6003
23.15 −2.00000 − 3.46410i 9.51560 + 16.4815i −8.00000 + 13.8564i −21.3469 + 36.9739i 38.0624 − 65.9260i 85.6895 − 148.419i 64.0000 −59.5934 + 103.219i 170.775
23.16 −2.00000 − 3.46410i 13.1333 + 22.7475i −8.00000 + 13.8564i −47.4488 + 82.1838i 52.5332 − 90.9901i −44.4079 + 76.9167i 64.0000 −223.467 + 387.056i 379.591
23.17 −2.00000 − 3.46410i 13.5829 + 23.5262i −8.00000 + 13.8564i 24.4390 − 42.3296i 54.3315 − 94.1048i 9.60315 − 16.6331i 64.0000 −247.488 + 428.663i −195.512
55.1 −2.00000 + 3.46410i −13.6586 + 23.6574i −8.00000 − 13.8564i 17.9261 + 31.0490i −54.6345 − 94.6297i 88.5343 + 153.346i 64.0000 −251.616 − 435.811i −143.409
55.2 −2.00000 + 3.46410i −12.8762 + 22.3023i −8.00000 − 13.8564i −34.0549 − 58.9848i −51.5049 − 89.2091i −41.6938 − 72.2158i 64.0000 −210.095 − 363.895i 272.439
55.3 −2.00000 + 3.46410i −11.1218 + 19.2635i −8.00000 − 13.8564i 6.81513 + 11.8042i −44.4872 − 77.0540i 73.6066 + 127.490i 64.0000 −125.888 − 218.045i −54.5211
See all 34 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 23.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
79.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 158.6.c.a ✓ 34
79.c even 3 1 inner 158.6.c.a ✓ 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
158.6.c.a ✓ 34 1.a even 1 1 trivial
158.6.c.a ✓ 34 79.c even 3 1 inner